Algebra worksheet — GCSE Higher

1.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

2.By completing the square, find the turning point of the curve y = x² + 6x + 2.

3.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

4.Solve x² − 100 = 0.

5.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.

6.Solve 2x² − 32 = 0.

7.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

8.A machine bought for £2,400 loses 12% of its value every year. After how many complete years does its value first fall below £1,500?

9.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

10.Make x the subject of the formula y = 3(x + 2).

11.A proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?

12.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

13.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

14.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

15.Solve x² − 6x = 0.